In recent years, with development of modern power system and the widespread use of power electronics technology, the electrical power load structure has undergone significant changes. A large number of non-linear power loads from applications of electric arc furnaces (EAFs), electric railways, thyristor-based voltage and frequency adjustment devices have become the main harmonic sources in a power grid, which input a large amount of harmonic currents into the power system and may lead to voltage waveform distortion in the power grid. Harmonics may, to different extents, adversely affect the normal operations of a variety of electrical equipment in the power system. Among them, the influence of harmonics on the capacitor bank is especially serious, which mainly includes increase of power loss in capacitor bank, harmonic resonance formed in the capacitor bank circuits, magnification of harmonic currents, and a shorter service life of capacitor bank.
Operating experience proves that harmonics in power grid are increasingly endangering capacitor bank and series reactor, and fire accidents caused by the failure of capacitor bank and series reactance in the substations occur frequently. The current methods used for the capacitor protections include differential voltage protection, differential current protection, overcurrent protection, overvoltage protection, and undervoltage protection, etc. However, only the fundamental waves of voltage and current are measured in these methods, the specific harmonic components are not measured and harmonic protections are not provided. Therefore, technical problems to be solved in this field include how to achieve a harmonic measurement and to send out an alarm signal or to disconnect a capacitor bank when the harm caused by the harmonic is more severe, such that the harmonic protection for capacitor can be realized to avoid the damage of the capacitor bank and to prevent the accidents from spreading or expanding.
The key to the harmonic protection for capacitor bank lies in the dense and accurate sampling of harmonics and the fast and accurate calculation. Currently, Discrete Fourier Transform (DFT) algorithm is often used in the calculation of harmonics:
      x    ⁡          (      t      )        =            ∑              n        =        1            ∞        ⁢          (                                    X            Rn                    ⁢          cos          ⁢                                          ⁢          nwt                -                              X            In                    ⁢          sin          ⁢                                          ⁢          n          ⁢                                          ⁢          wt                    )      
where, XRn is the real part of the n-th harmonic component, XIn is the imaginary part of the n-th harmonic component.
            X      Rn        =                  2        N            ⁢                        ∑                      k            =            1                    N                ⁢                              x            ⁡                          (              k              )                                ⁢                                          ⁢                      cos            ⁡                          (                              nk                ×                                                      2                    ⁢                    π                                    N                                            )                                                      X      In        =                            -          2                N            ⁢                        ∑                      k            =            1                    N                ⁢                              x            ⁡                          (              k              )                                ⁢                                          ⁢                      sin            ⁡                          (                              nk                ×                                                      2                    ⁢                    π                                    N                                            )                                          
where, N is the number of samples in every fundamental harmonic period. When n is taken on different values, the real part and the imaginary part of different frequency harmonic component can be calculated.
According to the formula Xn=√{square root over (XRn2+XIn2)}, the effective value of the n-th harmonic can be obtained. It is generally believed that the equation for calculating the current effective (or RMS) value of the capacitor bank is
      I    =                            I          1          2                +                              ∑                          n              =              2                        ∞                    ⁢                      I            n            2                                ,
It is found from the actual operation that the results from the described algorithm are often lower than the actual current RMS value, therefore protection device often cannot disconnect the capacitor bank promptly, and then the malfunction expands.